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lorasvet [3.4K]
3 years ago
6

A football coach gives half his players a protein bar to eat before each game; the other players do not receive the protein bar.

After a month of games, he analyzes their playing stats. He concludes the protein bar helped improve their performance on the field. How can the coach test the means to be sure the results are not likely to happen by chance?
Mathematics
1 answer:
timofeeve [1]3 years ago
4 0
To make the sure the results did not happen by chance, the coach can ensure that the protein bars are the only difference between the two groups. For example, he can make sure that both groups are drinking the same amounts of water and getting in the same amount of practice; that way, he will be able to determine that one group is performing better due to the protein bars only. Also, the coach can repeat this experiment multiple times to make sure that the results weren't a random, one-time thing. 
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Solve the system of linear equations.
sweet-ann [11.9K]

Answer:

  • dependent system
  • x = 2 -a
  • y = 1 +a
  • z = a

Step-by-step explanation:

Let's solve this by eliminating z, then we'll go from there.

Add 6 times the second equation to the first.

  (3x -3y +6z) +6(x +2y -z) = (3) +6(4)

  9x +9y = 27 . . . simplify

  x + y = 3 . . . . . . divide by 9 [eq4]

Add 13 times the second equation to the third.

  (5x -8y +13z) +13(x +2y -z) = (2) +13(4)

  18x +18y = 54

  x + y = 3 . . . . . . divide by 18 [eq5]

Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:

  y = 3 -x . . . . solve eq5 for y

  x +2(3 -x) -z = 4 . . . . substitute into the second equation

  -x +6 -z = 4

  x = 2 - z . . . . . . add x-4

  y = 3 -(2 -z)

  y = z +1

So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...

  x = 2 -a

  y = 1 +a

  z = a

_____

<em>Check</em>

First equation:

  3(2-a) -3(a+1) +6a = 3

  6 -3a -3a -3 +6a = 3 . . . true

Second equation:

  (2-a) +2(a+1) -a = 4

  2 -a +2a +2 -a = 4 . . . true

Third equation:

  5(2-a) -8(a+1) +13a = 2

  10 -5a -8a -8 +13a = 2 . . . true

Our solution checks algebraically.

6 0
3 years ago
A recent study at UGA (March 5, 2008) suggests that students with cell phones may take more risks than students that do not have
Ira Lisetskai [31]

Answer:

(a) -2.8

b) (1) Reject H0: p = 0.50 in favor of HA: p < 0.50; there is sufficient evidence to conclude that less than half of all UGA female students who, if they had a cell phone, would be willing to walk somewhere after dark that they would normally not go.

Step-by-step explanation:

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

H0: p = 0.50

This means that:

\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5

In a random sample of 305 UGA female students, 128 responded that, if they had a cell phone, they would be willing to walk somewhere after dark that they would normally not go.

This means that n = 305, X = \frac{128}{305} = 0.4197

a) Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.4197 - 0.5}{\frac{0.5}{\sqrt{305}}}

z = -2.8

Pvalue:

We are testing the hypothesis that the proportion is less than 0.5, which means that the pvalue of the test is the pvalue of z = -2.81.

Looking at the z-table, z = -2.8 has a pvalue of 0.0026

(b) What is the correct conclusion for this hypothesis test at the 0.05 level of significance?

0.0026 < 0.05, which means that we reject the null hypothesis, that the proportion is 0.5, and accept the alternate hypothesis, that the proportion is less than 0.5, option (1).

6 0
3 years ago
Write 0.326 in two other forms
Zepler [3.9K]

Answer:

1). 0.026

2) 0.300

Step-by-step explanation:

7 0
3 years ago
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A painter leans a 15-ft ladder against a house. The base of the ladder is 5ft from the house. A: To the nearest tenth of a foot,
Dvinal [7]

Answer:

14.1 feet

Step-by-step explanation:

Draw a diagram to get a triangle, and label it. use the pythagorean theorem, a^2+b^2=c^2

6 0
3 years ago
Please help me I don’t understand
Delvig [45]

Answer: I don't understand either :{

But I do know that you have to look at the little letters to answer the questions about the triangle. Like when it asks, "What are the possible values for x?" you have to find x then say what the possible values for x are. Hope that helps a little bit

3 0
3 years ago
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